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Different Variances?

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  • This topic has 30 replies, 10 voices, and was last updated 13 years ago by A.S..
Viewing 31 posts - 1 through 31 (of 31 total)
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  • #46510

    Allthingsidiot
    Participant

    Determine whether the  following 2  types of rockets  have  significantly different variance at  the  5% level?
    Rocket A
    61 readings
    1.347 miles
    Rocket B
    3 readings
    2.237 miles

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    #153841

    ratios and df
    Participant

    look at the ratios and the degrees of freedom … you don’t even have to look up the F-values in a table, it’s so obvious :-).

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    #153847

    A.S.
    Participant

    Is it correct to compare 63 readings and 3 readings?
    Is there any logic in sample sizes?
     

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    #153848

    Allthingsidiot
    Participant

    Agree
    It  is  31  readings  for  the  second  rocket
    Thanks for  your  kind  observation

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    #153851

    Jim Shelor
    Participant

    Assuming 1.347 and 2.237 are the sigmas, yes the variances are significantly different.
    If 1.347 and 2.237 are the variances, there is insufficient evidence to conclude that the variances are significantly different.

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    #153852

    Mikel
    Member

    Wrong – show your work.

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    #153855

    Jim Shelor
    Participant

    Stan,
    Problem 1.
    Test for Equal Variances – Assume 1.347 and 2.237 represent variances.
    95% Bonferroni confidence intervals for standard deviations
    Sample N Lower StDev Upper
    1 61 0.96281 1.16060 1.45520
    2 31 1.15891 1.49566 2.08983
     
    F-Test (normal distribution)
    Test statistic = 0.60, p-value = 0.095
    p-value > alpha, fail to reject null, insufficient evidence to conclude a difference exists.

    Problem 2
    Test for Equal Variances – Assume 1.347 and 2.237 represent sigmas.  Therefore, variances are 1.814 and 5.004 respectively.
    95% Bonferroni confidence intervals for standard deviations
    Sample N Lower StDev Upper
    1 61 1.11732 1.34685 1.68872
    2 31 1.73331 2.23696 3.12562
     
    F-Test (normal distribution)
    Test statistic = 0.36, p-value = 0.001
    p-value < alpha, reject null, a significant difference exists between the variance of rocket A and rocket B.
    Now show your work.

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    #153857

    ratio and f value
    Participant

    The question asks if the variances are equal. As a result one simply divides the larger variance by the smaller variance, i.e.2.237/1.347 and looks up the critical value of the F-statistics for d.f = 30 and d.f = 60. The critical ratio exceeds the calculated test statistic (you don’t even have to look that up given how close the ratio is to one). As a result you reject the null hypothesis. Remember, this is a question asked by “Allthingsidiot”. So the answer cannot be that complicated :-).

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    #153858

    Jim Shelor
    Participant

    ratio and f value,
    Assuming 1.347 and 2.237 are the variances (the numbers are not labelled so they cound be standard deviations), the ratio 2.237/1.347 = 1.66, I do not consider than very close to 1.
    Working this in Minitab, I get the opposite answer from the one you get.  I fail to reject the null, there is insufficient evidence to conclude there is a difference in the variances.
    Test for Equal Variances – Assume 1.347 and 2.237 represent variances.
    95% Bonferroni confidence intervals for standard deviations
    Sample N Lower StDev Upper
    1 61 0.96281 1.16060 1.45520
    2 31 1.15891 1.49566 2.08983
    F-Test (normal distribution)
    Test statistic = 0.60, p-value = 0.095
    p-value > alpha, fail to reject null, insufficient evidence to conclude a difference exists.

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    #153860

    ratio f test
    Participant

    to my knowledge the 2sample variance technique under Basic Statistics asks you for the raw data, not summary data and degrees of freedom. With 30 and 60 degrees of freedom respectively your critical F value is 1.82, i.e, higher than the calculated value. Did you look the two sided test up, i.e. split 0.05?

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    #153862

    Mat Maccallum
    Participant

    1.66 is “close to” 1 when the sample sizes are 60 and 30. you would be right if the sample sizes where larger. You can prove this by getting a large real world data set finding the Stdev then getting the ratio of stdev for alot of sample sets of size 60 and 30. The ratio will be less than 1.82 95% of the time.

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    #153865

    Jim Shelor
    Participant

    The Minitab 14 test for equal variances undeer basic statistics asks for summary data consisting of sample size and variance.
    It calculates using the two sided alternative.
    You can see the printout in my last post.
     
    An F-Ratio Test using Excel yields:
    Inputs sample 1 – 61 samples, 1.347 variance
    Inputs sample 2 – 31 samples, 2.237 variance
    Test Statistic – 0.6021
    2 sided 2 sample cutoff values – lower 0.5509, upper 1.9400
    Test statistic is > lower and < upper.
    Fail to reject the null, insufficient evidence to conclude a difference in the variances.
     
    How about somebody else showing their work instead of simply stating the answer is obvious.

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    #153867

    ratio
    Participant

    What’s the disagreement? You used Minitab, I used the F table. There is no other work to show. It’s a very simple F-test …

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    #153868

    Jim Shelor
    Participant

    The difference is:
    Your answer is reject the null.
    My answer is fail to reject the null.

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    #153869

    ratio
    Participant

    If you had grown up using the F table to look up the critical values prior to the advent of computer software programs, you’d also simply “know” what the cut-off points for various combinations of degrees of freedom are. One small little observation though: 60 and 30 are the degrees of freedom. The corresponding samples are 61 and 31 (as in the original post). So you may have to adjust that ratio slightly … the devil’s always in the detail, and in statistics this little attention makes the difference between someone who knows … and someone who “knows” :-).  

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    #153870

    ratios
    Participant

    Fail to reject the null, insufficient evidence to conclude a difference in the variances.
    With 30 and 60 degrees of freedom respectively your critical F value is 1.82, i.e, higher than the calculated value.
     
    I’ll gladly look up the calculations in Minitab and compare them with my look up (very superficial indeed, but sufficient to come to the right conclusion), but if the cut-off value is higher than the calculated value, I would assume that everyone who has had basic statistics knows that this means that you fail to reject the null hypothesis :-))))). How much more basic can it get?

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    #153871

    Allthingsidiot
    Participant

    Thank You  for  make  me  Laugthing??

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    #153872

    ratio
    Participant

    Your grammar will never improve: “Make me laugh” … but I am getting a kick out of this too … so much confusion about the simplest of all of the hypothesis tests …

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    #153874

    Jim Shelor
    Participant

    Then why did you say to reject the null in your post?

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    #153873

    Allthingsidiot
    Participant

    Ratio
    You

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    #153875

    Allthingsidiot
    Participant

    Ratio
    Again  thank  you.
    You  can’t  blame  me  because  I’m  “Allthingsidiot” as  you  have  recognized.I’m  glad  that  my  “stupid”  question  has  initiated such  intelligence debate,attracting  clever and  smart  people  like  you  and  the  others,please  proceed  forward 

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    #153876

    Mikel
    Member

    Jim, why did you use 60 and 30 for df?It should be 60 and 2 – learn to read please.

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    #153877

    ratios
    Participant

    oops … that’s correct, fail to reject … okay the tag’s on my :-).

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    #153878

    Jim Shelor
    Participant

    Because the second post from Allthingsidiot changed the sample size to 31?
    It

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    #153879

    Jim Shelor
    Participant

    Because the second post from Allthingsidiot changed the sample size to 31?
    It be

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    #153881

    Jim Shelor
    Participant

    Because the second post from Allthingsidiot changed the sample size to 31?
    It be I all

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    #153882

    ratio
    Participant

    sure, and continue to dream to get a job in six sigma with your Villanova University certificate … glad I can do something to brighten your obviously very sad and delusioned life :-))))).

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    #153883

    Jim Shelor
    Participant

    Sorry about the multiple posts, I do not know how I did that.

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    #153880

    Jim Shelor
    Participant

    Because the second post from Allthingsidiot changed the sample size to 31?
    It be I

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    #153891

    Allthingsidiot
    Participant

    Stan
    I  couldn’t  expect  you  to  ask  such a ”           ” question?

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    #153914

    A.S.
    Participant

    Is there any criteria for sample size while doing comparative study F 0r T test etc
    Sample need not be same size?
    If difference in sample size is allowed,how much?
     
     

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